This invention is in the field of electromagnetic reflectors, and is particularly concerned with beam-shaping reflectors for optical radiation (light). Such reflectors are used to produce a collimated or other shaped beam from a point source, or may be used to focus collimated or other rays. Typical examples of the shapes of such reflectors are spherical, parabolic, and arrays of plane reflectors. U.S. Pat. No. 52,987 of Mar. 6, 1866 is an example of such a reflector. In order to produce a beam of a certain divergence from a point source, to which the invention is specifically directed, the usual ways are to employ an aperature in the source housing, or to employ a parabolic reflector with the source at the focus of the reflector and with an aperature to define the desired beam. The chief disadvantage with these ways is that only a portion of the light from the source falls in the desired beam. Obviously, one might employ the combination of a parabolic reflector to collimate all of the light from the source and a diverging lens to yield the desired beam angle. This combination is both more complex (two elements) and more expensive (parabolic reflector) than the inventive reflector, which uses only conic sections.